Difficult# Computing Derivatives of Composed Function, Given a Table

APCALC-LF69ZY

Let the differentiable functions $F(x)$ and $G(x)$ have the values given in the table below.

Define $H(x)=F(G(x))$. For which value(s) of $a$ and $b$ does $H'(a)=H'(b)$?

I. $a = 2$ and $b = 8$II. $a = 4$ and $b = 6$III. $a = 2$ and $b = 6$